Augmented sixth chord

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The interval of an augmented sixth normally resolves outwards by semitone to an octave.

An augmented sixth chord contains the interval of an augmented sixth above its bass. The chord had its origins in the Renaissance,^[1] was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.^[2]

The augmented sixth interval is typically between the sixth degree of the minor scale and the raised fourth degree: ♭6–♯4. The chord is then usually followed directly or indirectly by some form of the dominant chord, in which both notes have moved to the fifth degree of the scale. This tendency to expand outwards to the octave is why the interval is spelled as an augmented sixth rather than enharmonically as a minor seventh. Although such an augmented sixth chord is more natural in the minor mode, it also came to be used in the major mode by borrowing the flattened sixth degree of the parallel minor scale.^[3]

There are three standard types of augmented sixth chord, each named after a European nationality, although the names are irrelevant to their origin and function. Theorists have struggled for centuries to explain the origins of these chords, define their roots, and fit them into conventional harmonic theory.^[4]

These chords are sometimes used with a different augmented sixth interval from ♭6–♯4, or with a different member of the chord in the bass, or both.

[edit] Function of augmented sixth chords

The different varieties of augmented sixth chord have the same function harmonically: as altered supertonic or subdominant chords leading to a dominant chord. This movement to the dominant is heightened by the chromatic raising of the fourth scale degree (F♯ in c minor). This characteristic has led many analysts to describe augmented sixth chords as variants of the secondary dominant V of V. In the major mode, the chromatic effect is more pronounced, because while the minor scale already has a minor sixth degree (♭6), the major has a major 6, so the augmented sixth introduces two chromatically altered tones, rather than just one.

[edit] Italian sixth

The Italian sixth moving to V

The Italian sixth (It ^{+ 6} or It⁶) is derived from chord iv⁶ with a raised fourth degree (scale degrees ♭6, 1 and #4; A♭–C–F# in C minor.) This is the only augmented sixth chord comprising just three notes; in four-part writing, 1 is usually doubled, because it is the only stable member of the chord.

[edit] French sixth

The French sixth chord; the distinguishing tone is highlighted in blue.

The French sixth (Fr ^{+ 6} or Fr) is like the Italian, but with an additional tone on scale degree 2 (♭6, 1, 2, ♯4). This creates a sonority that is both enharmonically inversionally reflexive and enharmonically equivalent to itself transposed at the tritone.

In the late Romantic period, the French sixth gained more significance, since because of its equivalence to itself at the tritone it could be used not only to resolve to V, but also to ♭II, the Neapolitan sixth. This enabled modulation to rather distant keys: a significant means of expression for Romantic composers.

[edit] German sixth

The German sixth; the distinguishing tone is highlighted in blue.

The (Gr ^{+ 6} or Ger) is also like the Italian, but again with an added tone, this time on scale degree ♭3 (♭6, 1, ♭3, ♯4). It is enharmonically equivalent to a dominant seventh, specifically the applied dominant V of ♭II. Thus, like the French sixth, it was often used in this relationship by Romantic composers as a method of modulation to remote keys. In Classical music, however, it appears in much the same places as the Italian sixth, though it is less used, perhaps because of the contrapuntal difficulties outlined below. It appears frequently in the works of Beethoven.

The German sixth is typically followed by a 6/4 chord to avoid parallel fifths.

It is difficult to avoid parallel fifths when proceeding to V. Although these parallel fifths were occasionally accepted by common practice composers (and referred to as Mozart fifths), there are two ways they are avoided:

• The chord can move to a "cadential six-four" chord (whether this is thought of as an intensification of V or a second inversion of I); this, in turn, is normally followed by a root-position V. This resolution allows for two common notes (when resolving to a minor chord or tonic), or one common note (for major). Composers often then respell the ♭3 enharmonically as ♯2, to ensure proper voice leading to 3 in the next chord. This doubly augmented or ♯2 respelling of the German chord allows it to be approached and resolved like the French chord, with frequent motion to through the cadential 6/4 chord. On account of this mixing of national characters, the chord is sometimes called the English augmented sixth, or the "Swiss" or "Alsatian" chord.^[5]

German sixth chord respelled with doubly augmented fourth (highlighted in blue) for voice-leading purposes

• The chord can be converted to the Italian or French version just before resolving to V.^[6]

An example of Gr ⁺ 6 can be found in the high passage heard twice in the "Passepied" from Debussy's Suite Bergamasque.

An example of a German sixth chord from Michael Haydn's Requiem in C minor, first movement ( Listen)

[edit] Roots of augmented sixth chords

Theorists vary in their treatment of the roots of augmented sixth chords.

[edit] Inversions of augmented sixth chords

Augmented sixth chords are occasionally used with a different chord member in the bass. Since there is no consensus among theorists that they are in root position in their normal form, the word inversion isn't necessarily accurate, but some textbooks use it nonetheless. Composers often use such positions because the voice-leading calls for them. For an excellent example, see Tchaikovsky's, Symphony no. 5 (op. 64, I), Allegro con anima (bars 3–4).

Excerpt from Bach's Mass in B minor

The example shows an augmented sixth chord in inversion used by Bach. At the end of the second measure of the example, the augmented sixth (here inverted to a diminished third or tenth), is between the bass and the soprano; these two voices resolve inward to an octave. This form of the chord, if in its usual position, would be a German sixth chord.

[edit] Augmented sixths on scale degrees other than ♭6

Occasionally the lowest note of the augmented sixth interval is on a different scale degree. Most often, this results from a temporary tonicization, and the resulting augmented sixth chord is borrowed from the key of the secondary dominant which follows it. However, there are a few examples in the literature of these chords appearing without such a context. Schubert used it in some of his last compositions, in dramatic final cadences.

Augmented sixth chord on scale degree ♭2 in Schubert's piano sonata D. 959. Italian form, preceded by a Neapolitan sixth chord in root position.

[edit] Augmented sixth chords in the literature

The second movement of Beethoven's piano sonata in F-sharp major, op. 78, begins with an Italian sixth chord:

Richard Wagner's famous Tristan chord (indicated below with Tr) is often analyzed as a French sixth with an upwardly resolving appoggiatura in the upper voice:

[edit] Other aspects of augmented sixth chords

Augmented sixth chords with compositions other than those shown above are sometimes seen, and they too are sometimes given whimsical geographical names. For example, a chord comprising 4, ♭6, 7, and ♯2 is called by one source an Australian sixth.^[7] Like some of the chords examined earlier, such innovations as these usually have alternative interpretations.

In jazz, the French augmented sixth chord would typically be described as a tritone substitution, and spelled as a dominant chord. Tritone substitutions are used more freely in jazz than augmented sixth chords are in common practice style. From a jazz perspective, the French form on ♭6 would be seen as a specific idiom for V⁷ of V, used mainly in the minor mode.

A tritone sub however generally functions as a dominant substitution, whereas an augmented sixth chord has predominant function. For example, a typical french augmented sixth chord in the key of C major would be spelled as D F# Ab C, and would resolve to a G chord, the dominant. Because a tritone substitution is a substitution for dominant itself, we must think of it a little differently. A tritone sub enharmonic with a standard Fr+6 in C would actually be a V+11/V -- V augmented 11 of V, or an altered secondary dominant, with the eleventh factor in the bass, Spelled: D F# C G#. This being the most common voicing for an augmented eleventh chord (root, third, seventh, and augmented eleventh.) There are several other possible chord qualities for a tritone sub as well.

[edit] See also

• Chord progression
• Diatonic function
• Neapolitan sixth
• Tristan chord

[edit] Notes

1. ^ Andrews, HK, The Oxford harmony, Vol. 2, OUP, 1950, pp. 45–46.
2. ^ Andrews, HK, op. cit., pp. 46–52.
3. ^ Aldwell, E, and Schachter, C, Harmony and voice leading, 2nd ed., Harcourt Brace Jovanovich, San Diego, 1989, pp. 478–83.
4. ^ Some general sources for the modern theory of these chords are Aldwell and Schachter (op. cit.); Gauldin R, Harmonic practice in tonal music, Norton, New York, 1997, ISBN 0-393-97074-4, pp. 422–438; and Christ, W, DeLone, R, Kliewer, V, Rowell, L, and Thomson, W, Materials and structure of music, Vol. 2, 2nd ed., Prentice-Hall, NJ, 1973, pp. 141–171. (Christ et al. offer a usefully detailed consideration of augmented sixth chords along with the Neopolitan sixth chord.)
5. ^ The respelled chord is sometimes illogically called a "doubly augmented sixth chord"; but the fourth between ♭6 and ♯2 (such as A♭ to D♯ in C major) is the interval that is doubly augmented.
6. ^ Benjamin, T, Horvit, M, and Nelson, M, Techniques and materials of music, 7th ed., Thomson and Schirmer, 2008 [sic], p. 165. Beethoven frequently moves from one form of the chord to another in such a way, sometimes passing through all three.
7. ^ Burnard, Alex, Harmony and composition, Allans Music (Australia), 1950, pp. 94–95.